Speaking Stata: The limits of sample skewness and kurtosis

Abstract. Sample skewness and kurtosis are limited by functions of sample size.
The limits, or approximations to them, have repeatedly been rediscovered over
the last several decades, but nevertheless seem to remain only poorly known. The
limits impart bias to estimation and, in extreme cases, imply that no sample could
bear exact witness to its parent distribution. The main results are explained in a
tutorial review, and it is shown how Stata and Mata may be used to confirm and
explore their consequences.